Stabilization of generalized Hamiltonian systems with dissipation is investigated. First, we generalize the Casimir submanifold approach with constant controls to the static state feedback control case. Secondly, a direct Hamiltonian function method is proposed and it is shown that this method is equivalent to the Casimir sub-manifold approach. Furthermore, a dynamic state feedback control is proposed. Some sufficient conditions and a constructive process for determining cont rollers are provided. It is shown that the dynamic state feedback control is more powerful than the static one. Finally, the problem of a dissipative type realization of the general controlled Hamiltonian system is discussed.